It's tricky because I use AI for work quite often to refine what I want to say when I have some writer's block. So I will type in what I want to say even if I know it's not worded well and it normally refines it.
I always make changes to what is produced but I wouldn't copy over any text to an essay for uni because of the risk of copying code.
There is a "way" some AI tools write though which introduce Americanisms not used widely in British English. A few times I've noticed what it's come up with is "off" in tone but without being able to put my finger on why. Then there's the ubiquitous "em dash" and words like "quietly" which it seems to love.
Definitively prove it? I have no idea. But especially as it's new, I'm sure lecturers can see sudden changes in style and be suspicious right now. But I think Linkedin is showing the way it might go. If you are on Linkedin much you will see how ubiquitous AI posts are. Even if you can't pin exactly why, you know. And the common thread is? They're really boring. What is now starting to stand out (at least on my feed) is the slightly messy, but authentic. It does make me wonder whether an AI produced essay might get you a 2(ii) or 2(i) grade in an essay but no higher.
Lastly and this is the big kicker for uni work, AI searches for references? Just don't go there. They are sometimes plain wrong, don't exist or don't reference what it claims they do. Or it's a really minor study which is so niche and against the prevailing research. If you get AI to write it all then that's what you'll get and it will be incredibly obvious.
Where I think you could use AI and get away with it is to ask how to structure your work, what sections to include etc and then, without copying that, use that as a basis.